Describing variance with a simple water quality model and hypothetical sampling programs

An explicit treatment of the uncertainty in the state of water quality in a body of water can provide a quantitative basis for sampling decisions. Filtering theory, an extension of Bayesian analysis to dynamic systems, is used to obtain an algorithm which describes the time history of variance (uncertainty) in estimates of water quality parameters. Uncertainties arising from measurement errors, incompleteness of data, and random fluctuations exhibited by natural phenomena are taken into account. Sampling design capabilities are illustrated in an evaluation of sampling frequencies for the National Eutrophication Survey. The adequacy of any sampling program is dependent on the available prior data and on the value associated with reductions in uncertainty.